8.9. Predictor-Corrector Methods — Coming Soon

References:

• Section 6.7 Multistep Methods in [Sauer, 2019].

• Section 5.6 Multistep Methods in [Burden et al., 2016].

Introduction

We have seen one predictor-corrector method already: the explicit trapezoid method, which uses Euler’s method to predict a first approximation of the solution, and then corrects this using an approximation of the implicit trapezoid method.

We will look at combining the \(s\)-step Adams-Bashforth and Adams-Moulton methods to achieive an two-stage, \(s\)-step method of same order of accuracy as the latter while being explicit — the explicit trapezoid method is this in the simplest case \(s=1\).

import numpy as np
from matplotlib import pyplot as plt
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from matplotlib.pyplot import figure, plot, grid, title, xlabel, ylabel, legend